nehalkapadi123 wrote:
Seven students each bought some books on a book fair. Is the total number of books they bought greater than 27?
(1) No student bought more than 7 books.
(2) No two students bought same number of books.
Target question: Is the total number of books they bought greater than 27? Given: Seven students each bought some books on a book fair. IMPORTANT: On the GMAT, "some" means "
1 or more"
Statement 1: No student bought more than 7 books. There are several scenarios that satisfy statement 1. Here are two:
Case a: The number of books that each of the 7 people bought are {6,6,6,6,6,6,6}. A total of 42 books were bought. So, the answer to the target question is
YES, the total number of books bought IS greater than 27Case b: The number of books that each of the 7 people bought are {1,1,1,1,1,1,1}. A total of 7 books were bought. So, the answer to the target question is
NO, the total number of books bought is NOT greater than 27Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: No two students bought same number of booksSo, all 7 values are DIFFERENT.
Let's determine the FEWEST number of books that could have been purchased by each person.
Well, the fewest books a single person can buy is 1.
So, the fewest books the next person can buy (if duplication is not allowed) is 2
Then 3 etc
So, the FEWEST books bought happens when the number of books bought are {1,2,3,4,5,6,7}
1+2+3+4+5+6+7 = 28
So, the TOTAL number of books bought must be AT LEAST 28
This means the answer to the target question is
YES, the total number of books bought IS greater than 27Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent